Risk vs Reward: A Quantum Hawk-Dove Game and the Financial Crash of 2008

In a paper uploaded to the Arxiv in April, a group of researchers headed up by Matthias Hanauske, approach the recent financial meltdown from a Quantum Evolutionary point of view. Here’s the abstract:

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the ‘rules of the game’ in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non aggressive quantum strategy.

The Hawk-Dove game is a classic of Evolutionary Game Theory and has been applied in many varied ways all over the study of animal (and human) behavior. So, their use of it to study markets is nothing new. What IS new is taking a Quantum approach to this old game as a way of studying a method by which we can introduce regulations (a rule system) to the game of financial economics that would mitigate the kinds of behaviors that lead to the situation we’re in now. Don’t worry, it doesn’t require that we all spend our lives staring at quantum computers!

FINANCIAL RISK AND AGGRESSION

In the lead up to the financial crisis of 2008, certain actors in the market can be said to have exhibited aggressive behavior since they made choices that benefited only their own short term utility while KNOWING that these choices would negatively affect the utility of the group (all of us) as a whole. That is, these actors knew that these risky financial products would do harm to the overall market portfolio (and therefore be harmful, long term, to themselves), but would, in the short term, result in a positive gain to themselves–so they took them on anyway.

Given that we’re approaching economics like a game as it is, can we change the “rules” of this game so that aggressive behavior of the type discussed above is lessened? If this behavior is “natural” given the situation, then we certainly can’t expect people to play nice. We ought to do as the Boy Scouts do, “Hope for the best. Plan for the Worst.”

QUANTUM GAMES TO THE RESCUE

The authors show that dependent upon the type of entanglement, evolutionarily stable strategies (ESS’s) can show up that would NOT have been predicted by classical evolutionary game theory. What I love about their approach is they are not restricting themselves to a literalist interpretation of quantum game theory (that is, games played over quantum channels with tiny molecular objects as the unit of information). Instead, they are using this theory “metaphorically”.

That sounds bad. But, in truth ALL mathematics is metaphoric. A wave equation is not itself a wave. It just represents a wave. So, it’s not a stretch to take a mathematical idea that was originally strictly defined with respect to a particular physical situation, and apply it to a totally different situation. This has been the history of how great ideas in applied mathematics proliferate.

Here is how they set it up:

“We interpret entanglement in this context as the objective influence of socio-economic context factors, while the application of quantum strategies exhibits the degree to which decision makers incorporate these factors into their decisions. This interpretation allows the derivation of consequences and shows the linkage of our study to other game theoretical analyses that also highlight the importance of the socio-economic context to the outcomes of games.”

But, first let’s look at the classic (non-quantum) evolutionary game as applied to the financial crisis.

They call the Doves in the game those bank investors who acquire rather low risk products that return moderate payoffs. The Hawks are those bank investors who seek out high risk products that have the potential to return large payoffs–but, these also could result in huge losses. The authors make the point:

“Additionally, when selling their products to investors, doves remain with their contract conditions and do not try to make a deal by all means, e.g. promising unrealistic returns or omitting to point out severe risk factors of the investment product.”

Hawks do whatever necessary to make a profit.

Both of these investors then fight to garner the attention of a more moderate or neutral group of investors. When a hawk “fights” a dove, the hawk wins, since he can offer a higher return to the investor. If 2 doves fight, then the investor splits his investment equally among them assuming they will both return an equal amount. If 2 hawks meet, the investment is again spread equally.

The payoffs of all three situations are different as is true in the classical version of the game. I’m NOT going to get into what this actually looks like, as the math gets ugly, but it results in the following. The evolutionary game theoretic predictions of this particular version of the Hawk-Dove game are that the ratio of aggressive vs. non-aggressive behaviors would not reach equilibrium. That is, it predicts a crash!

OK, great. We already HAD the crash. What can we do to prevent it? That is:

“Although the risk of destabilization in the investment market was obviously increasing for the last few years, the behaviour of some aggressive investment bankers did not change. However, instead of ending in a stable state, finally the market crashed and almost all aggressive agents disappeared from the population. This could have been prevented, if any aggressive behaviour were inhibited completely.”

QUANTUM VERSION

They reformulated this game in a quantum game theoretic context and show that by entangling the strategies of the doves they induce a new Evolutionarily Stable Strategy that eliminates excessive hawkishness. By increasing the amount of entanglement (interconnectedness) the incentives to “go it alone” are reduced and the incentives to act in a more cooperative manner are increased.

The point is that regulations and social pressures that encourage openness and interconnectedness of market participants may be enough to drastically reduce aggressive and hawkish behaviors that lead to the type of destabilization seen in the recent market crash. In the lead up to 2008, there was very little entanglement of the strategies employed by market participants. This caused them to play the “game” in the classical way, a way that led inevitably to a market crash.

To reiterate, what’s great about this paper is their approach to using quantum game theoretic language OUTSIDE of a purely physical context:

“So far, in literature entanglement has been discussed from a more physical point of view. However, in order to derive consequences from the obtained results we want to propose one possibility to interpret it in an economic context. In this paper, entanglement has been termed a conjoint, psychological contract between the members of an economic population aligning their strategies. However, this contract is not the result of conscious negotiations but of general socio-economic factors influencing the agents simultaneously. These factors comprise moral standards, values, legal rules, joint experiences, a similar educational background etc. All these factors can drive the decision processes of different individuals into the same direction without the necessity that the individuals have to communicate to each other. The objective existence of these background factors can vary, which is reflected by the degree of the entanglement parameter .”

In Japan there is massive social pressure to be polite, at a level unheard of in America. In fact, it is so great, most American’s find it problematic and strange. It results in an entire culture avoiding certain types of behaviors they deem aggressive. We Americans wouldn’t think of these same behaviors as aggressive, per se. Instead, we value a type of forthrightness the Japanese find rude. As such, we exhibit behaviors seemingly more aggressive than they do.

The social pressures involved in Japanese culture can be seen as types of entanglement, since they correlate the strategies of the actors involved.

I think this is a fruitful way of looking at Quantum Game Theory applied to the social sciences and human behavior that better takes into account the socio-economic situations we all face, and how they affect our decision making than does classical game theory.